The HSE was responding to questions on how parents of children under-six in some blackspot areas - where there is poor take-up of the scheme - will cope.

New figures show there are 58,000 fewer people now covered by a full medical card compared to a year ago.

The fall comes amid ongoing resistance by many doctors to the Government scheme to give free GP visits to all under six year olds regardless of their parents income.

Several doctors believe it would be fairer to relax the means test for a medical card for low-income people. The HSE insisted yesterday that a significant factor in the fall in medical cards has been the rise in the numbers of people who had them that got jobs.

The number of GPs signing up nationally to the free visits for under-sixes scheme rose to 1,836 yesterday - 76pc of eligible doctors. But it is now looking increasingly likely that the poor take-up by GPs in south Tipperary and west Cork and Dublin south east will affect thousands of under-six year olds.

Other areas with lower coverage include Louth and Kildare as well as west Wicklow.

The HSE said yesterday that 46,500 of the 270,000 eligible children have been registered for the scheme to begin in the middle of next week.

A spokeswoman said the HSE will assign a GP to provide services to children under six in circumstances where a parent or guardian has been unsuccessful in getting three GPs to accept their child or children on to the a doctor's panel.

However, this will still mean that parents could face a considerable journey if they want their child to be seen for free.

Doctors in south Tipperary who are not to participate said they will charge a private fee and ask the parent to invoice the HSE.

Parents in Donegal, Galway, Laois and Offaly, north west Dublin, Sligo/Leitrim and Wexford will have the highest choice of GPs due to the numbers signing up.

Several GPs have taken Health Minister Leo Varadkar to task on Twitter, accusing him of a divide and conquer strategy to coerce GPs into signing.

Mr Varadkar replied that the GPs should "get on the train" and help in. He told the medics that GPs taking on the Government of the day is a "battle they can never win."

They needed to "cop on", said the minister, who worked as a GP until recent years.

Many GPs, however, remain convinced that the extra workload will affect their ability to deliver a same-day service to more of their older and sicker patients and will create waiting lists

Under the scheme, GPs will get an annual increased €125 capitation fee for each child under six regardless of how often they visit. This applies to new children they take on as well as capitation for each child under 6 existing and new patients to increase to €125. This is an 82pc increase in capitation. The current capitation fee is €68.65.

There are also top-up payments for children who have asthma. From September, GPs will start providing more care to adult patients with diabetes, offering them two clinical consultations which will include blood tests and a preventative lifestyle review.

Doctors who operate out-of-hours co-ops said children who need to see a GP during that time will not be charged even if the doctor has not signed up to the new scheme.